Question

Given the function, ƒ(x) = |x - 2| + 1, choose the correct range written using interval notation.

[-1, ∞)
(-∞, -1]
[1, ∞)
(-∞, 1]

Answer 1

[1,∞) Third one down.

Explanation:

Comment

A couple of notes so you know what we are looking for.

• (a,b) means that neither a nor b are included in the interval.
• [a,b] means that both a and b are included in the interval/
• Range means the y value.

Graph

The graph shows that the interval of the range is from 1 to infinity. Infinity is never part of a domain or a range. The bracket after infinity must be ( or ) depending on where infinity is. Nothing is eliminated by that fact.

The low point is 1, not minus 1. So the first and second choice are both incorrect.

The graph never crosses the x axis. - infinity cannot be even a limit of the interval. That makes the second and the last one incorrect.

Only the third one down is left. [1, ∞) is left. It is correct. 1 is part of the interval. Infinity is not.